148 research outputs found
Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators
Using the Lugiato-Lefever model, we analyze the effects of third order
chromatic dispersion on the existence and stability of dark and bright soliton
Kerr frequency combs in the normal dispersion regime. While in the absence of
third order dispersion only dark solitons exist over an extended parameter
range, we find that third order dispersion allows for stable dark and bright
solitons to coexist. Reversibility is broken and the shape of the switching
waves connecting the top and bottom homogeneous solutions is modified. Bright
solitons come into existence thanks to the generation of oscillations in the
switching wave profiles. Finally, oscillatory instabilities of dark solitons
are also suppressed in the presence of sufficiently strong third order
dispersion
Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
Bound states, also called soliton molecules, can form as a result of the
interaction between individual solitons. This interaction is mediated through
the tails of each soliton that overlap with one another. When such soliton
tails have spatial oscillations, locking or pinning between two solitons can
occur at fixed distances related with the wavelength of these oscillations,
thus forming a bound state. In this work, we study the formation and stability
of various types of bound states in the Lugiato-Lefever equation by computing
their interaction potential and by analyzing the properties of the oscillatory
tails. Moreover, we study the effect of higher order dispersion and noise in
the pump intensity on the dynamics of bound states. In doing so, we reveal that
perturbations to the Lugiato-Lefever equation that maintain reversibility, such
as fourth order dispersion, lead to bound states that tend to separate from one
another in time when noise is added. This separation force is determined by the
shape of the envelope of the interaction potential, as well as an additional
Brownian ratchet effect. In systems with broken reversibility, such as third
order dispersion, this ratchet effect continues to push solitons within a bound
state apart. However, the force generated by the envelope of the potential is
now such that it pushes the solitons towards each other, leading to a null net
drift of the solitons.Comment: 13 pages, 13 figure
Formation of localized states in dryland vegetation: Bifurcation structure and stability
In this paper, we study theoretically the emergence of localized states of
vegetation close to the onset of desertification. These states are formed
through the locking of vegetation fronts, connecting a uniform vegetation state
with a bare soil state, which occurs nearby the Maxwell point of the system. To
study these structures we consider a universal model of vegetation dynamics in
drylands, which has been obtained as the normal form for different vegetation
models. Close to the Maxwell point localized gaps and spots of vegetation exist
and undergo collapsed snaking. The presence of gaps strongly suggest that the
ecosystem may undergo a recovering process. In contrast, the presence of spots
may indicate that the ecosystem is close to desertification
Quadratic cavity soliton optical frequency combs
We theoretically investigate the formation of frequency combs in a dispersive second-harmonic generation cavity system, and predict the existence of quadratic cavity solitons in the absence of a temporal walk-off
Parametric localized patterns and breathers in dispersive quadratic cavities
We study the formation of localized patterns arising in doubly resonant
dispersive optical parametric oscillators. They form through the locking of
fronts connecting a continuous-wave and a Turing pattern state. This type of
localized pattern can be seen as a slug of the pattern embedded in a
homogeneous surrounding. They are organized in terms of a homoclinic snaking
bifurcation structure, which is preserved under the modification of the control
parameter of the system. We show that, in the presence of phase mismatch,
localized patterns can undergo oscillatory instabilities which make them
breathe in a complex manner
Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
We study the stability and bifurcation structure of spatially extended
patterns arising in nonlin- ear optical resonators with a Kerr-type
nonlinearity and anomalous group velocity dispersion, as described by the
Lugiato-Lefever equation. While there exists a one-parameter family of patterns
with different wavelengths, we focus our attention on the pattern with critical
wave number k c arising from the modulational instability of the homogeneous
state. We find that the branch of solutions associated with this pattern
connects to a branch of patterns with wave number . This next branch
also connects to a branch of patterns with double wave number, this time
, and this process repeats through a series of 2:1 spatial resonances. For
values of the detuning parameter approaching from below the
critical wave number approaches zero and this bifurcation structure is
related to the foliated snaking bifurcation structure organizing spatially
localized bright solitons. Secondary bifurcations that these patterns undergo
and the resulting temporal dynamics are also studied.Comment: 13 pages, 13 figure
Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators
In Ref. [Parra-Rivas at al., 2013], using the Swift-Hohenberg equation, we
introduced a mechanism that allows to generate oscillatory and excitable
soliton dynamics. This mechanism was based on a competition between a pinning
force at inhomogeneities and a pulling force due to drift. Here, we study the
effect of such inhomogeneities and drift on temporal solitons and Kerr
frequency combs in fiber cavities and microresonators, described by the
Lugiato-Lefever equation with periodic boundary conditions. We demonstrate that
for low values of the frequency detuning the competition between
inhomogeneities and drift leads to similar dynamics at the defect location,
confirming the generality of the mechanism. The intrinsic periodic nature of
ring cavities and microresonators introduces, however, some interesting
differences in the final global states. For higher values of the detuning we
observe that the dynamics is no longer described by the same mechanism and it
is considerably more complex.Comment: 11 pages, 9 figure
Locking of domain walls and quadratic frequency combs in doubly resonant optical parametric oscillators
The formation of frequency combs (FCs) in high-Q microresonators with Kerr type of nonlinearity has attracted a lot of attention in the past decade [1]. Recently it has been shown that FCs can be also generated in dissipative dispersive cavities with quadratic nonlinearities [2,3], opening a new possibility of generating combs in previously unattainable spectral regions. Previous work has shown that modulational instability (MI) induces pattern and FC formation in degenerate optical parametric oscillators (OPOs) [4]. However, the existence of dissipative solitons or localized structures (LSs) is still unclear
Self-pulsing and chaos in the asymmetrically driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis
We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics may include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. We have thoroughly characterized such dynamical states, their origin, and their regions of stability by applying bifurcation analysis and dynamical system theory. This approach has allowed us to identify and classify the instabilities, which are responsible for the appearance of different types of temporal dynamics
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